Abstract
During the past few years, batch service systems have attracted considerable attention due to their wide area of applications. In this present paper, we study a special batch service polling system (the so-called Israeli queue) with priorities. Different from the previous papers which focus on the performance analysis, we aim to investigate the strategic behavior of customers and optimal design for the underlying queueing model. By considering two levels of information (observable and unobservable) provided upon customers’ arrival, we, respectively, derive the equilibrium strategies of high-priority and low-priority customers, regarding the joining or balking dilemma. We also present some numerical examples to reveal the impacts of several parameters on the equilibrium strategies, together with some intuitive explanations. Finally, we formulate the revenue function of the service provider and present the Particle Swarm Optimization algorithm to seek the optimal service prices for the high-priority and low-priority customers to maximize the service provider’s revenue under the two levels of information.
Highlights
Nowadays, queueing models with batch services frequently encountered in practice and studies addressing the batch service queueing systems have been investigated extensively owing to their wide area of applications, such as the transportation systems, tourist services, and telecommunication systems
In tourist areas, sightseeing bus will start off while the bus is full of travelers. e second category is to deal with the batch service models with infinite batch size
We considered a special batch service polling system with priorities and investigated the strategic behavior of high-priority and low-priority customers, regarding the joining or balking dilemma, under the two levels of information
Summary
Nowadays, queueing models with batch services frequently encountered in practice and studies addressing the batch service queueing systems have been investigated extensively owing to their wide area of applications, such as the transportation systems, tourist services, and telecommunication systems. For more studies on priority queues, we may refer the interested readers to Drekic and Grassmann [6], Jouini and Roubos [7], Takagi [8], Atencia [9], and the reference therein To this end, we incorporate customers’ joining/balking decisions into a special batch service polling system with priorities. Erefore, we are interested in the following research questions: Q1: How do the strategic customers (high-priority and low-priority customers) make their joining/balking decisions under different levels of information (observable and unobservable cases)? Erefore, under the two levels of information, we distinguish the high-priority and low-priority customers, respectively, derive their joining/balking strategies, and present the equilibrium rates with respect to various system parameters by considering different scenarios. For more details on this topic, the interested readers are referred to Adiri and Yechiali [37], Hassin and Haviv [21], and Hassin [22], in which the authors give comprehensive reviews on the topic of pay-for-priority option
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